Fresnel model

[niklasharrysson]

At the Physically Based Shading course at Siggraph this year Naty Hoffman presented issues with established Fresnel models. Both how it's incorrect to use the physical Fresnel equations directly in an RGB renderer, and also how Gulbrandsens method for making the parameterization artist friendly in fact fails at this on several counts.
slides

In addition Laurent Belcour presented a new Fresnel model, that is more accurate than Schlick's approximation and still works well for both offline and real-time rendering.
slides & code

Since Standard Surface is using Gulbrandsens methods, and definitely needs to be usable and accurate for non-spectral renderers, this is something we need to look into. Should we move away from Gulbrandsens method? And if so, what should we use instead?

Feedback from the rendering community is much appreciated!

[belcour]

Many thanks for starting the discussion Niklas!

There are many questions that needs answers from the community to be able to nail the specifications of a good 'standard' Fresnel model. Here are a couple of points I found interesting:

• Are we (meaning the rendering community) interested in having grazing angle control? That could mean either producing goniochromatism (without interference effects) for cheap, or reproducing measured IORs materials, or other reason. I like the ability to tune it, but I don't know what artists think of this.
• Are we interested in having a 'standard' Fresnel model simpler (in the sense of Schlick, parametrized by R0 only) but closer to specific reflectances (for example matching specific dieletrics for low R0 but matching specific conductors for high R0).

[niklasharrysson]

For grazing angle control, from our side I would say yes absolutely. When it comes to Standard Surface we have had the edge tint control for a while now and I think artist will expect this to remain controllable in some form. But since we use Gulbrandsen now, it is not really artist friendly, for the reasons Naty points out. And in addition with the reparameterization into the full physical equations we end up using that in our non-spectral/RGB renderers, so it's a problem with accuracy as well (as pointed out by Naty).

I think ideally, on our side, we would like to keep the F0/F90 parameterization (with F90 I here mean "some" type of gracing control). But having F90 more intuitive and linear, and solve the inaccuracy caused by using single eta/kappa values in an RGB renderer.

Naty's conclusion was that going back to Schlick is the best choice in most cases. Just using generalized Schlick (F0/F90) would then be the simplest choice. But it gives the artist more freedom (maybe to much?) to produce non-physical results? For full control we would also need to expose the additional 'exponent' parameter. What are peoples experience with generalized Schlick? I know it's used in several other shading models, commercial and in-house.

[fpsunflower]

+1 to needing the grazing angle control. I would even argue that having a third parameter to control the transition between the two colors is also important in many cases.

For a bit of context from the Imageworks side, we started with the Gulbrandsen parameterization because we happened to be revamping our bsdf model around the same time the paper came out. After the model was pushed into production, one of our more vocal artists lobbied strongly for us adding a "generalized Schlick" artistic mode: F0+(F90-F0)*(1-cos(theta))^p. The arguments were similar to the ones Naty made in his talk. The most convincing one for me being that the fresnel curve is actually a place we can capture other aspects of the physics than the raw fresnel equations allow. As Naty alluded to, real materials used on set in VFX production are rarely (never?) pure metals but instead layers of metallic paint on top of lighter materials. These interactions would be super complex to model physically. However since we had already rolled out the other model, we had to leave it as our default - and we haven't revisited this since (the curse of backwards compatibility).

I've asked to see if we can crawl our in house material libraries to see how often the artists deviate from defaults (this is a bit involved to do well given the flexible nature of material inheritance and overrides, etc ...). I'll try to report back if we can come up with anything quantitative.

Just to summarize the models under consideration for the thread:

• Vanilla Schlick (R0 only)
• Generalized Schlick (with power control above) (R0, R90, p)
• Naty's model from his MAM talk (R0, R82)
• Gulbandsen model (R0, g)
• Laurent's model (which can fit several of the ones above from what I understand, including being a way to reparameterize the Gulbrandsen model)

Any others we should be thinking about? Many years ago, the Maxwell renderer added a specific control to their bsdf model for very similar reasons [1]. From my recollection of lurking on their forums in those days, I believe this was also an artist driven request that came from a desire to match painted props.

[1] https://nextlimitsupport.atlassian.net/wiki/spaces/maxwell/pages/22684122/Custom+Fresnel+curve+-+r2

[noj86]

I wanted to start by flagged that I haven't had the chance to dig deep into Laurent Belcour proposal but from what I've seen of the slides, it looks very interesting and it could present a great solution for the various opinions, including mine that i've posted underneath.

To me the fundamental question is what are we trying to achieve artistically. In VFX, we're trying to get as close as possible to the real world but with enough flexibility to create the impossible. For that reason, I would expect any reference shader (and therefore its fresnel parametrization) to use a method that guarantee the plausibility of the material over its absolute realism.
In that context, I believe that moving away from the full fresnel equation would be a mistake and here are some point why :

• Schlick Fresnel is never beneficial in a dielectric context. It uses the same artistic friendly parametrization (R0) as a full dielectric fresnel but without the accuracy. Considering that the vast majority of materials are dielectric materials, it seems a bit silly to me to reduce the dielectric materials accuracy for a few conductor materials.
• Generalized Schlick edge controls (R90) and any similar approach (R82) very often results in non plausible material due to many uninformed artists creating materials with lesser reflectance towards the grazing angle than towards the incident angle.
• Making a decision on Fresnel based on a small set of pure material scan is not beneficial against the vast majority of completely random materials created by artists. It also important to acknowledge that 'reference' scanned material are only as good as the scan itself. This is also why there is a substantial amount of variation in the scan data depending on the source of the data.
• An approximation will always be an approximation. We have the full equations, I would vouch for more research on how to improve its artistic parametrization instead of reverting to an approximation.

For those reasons, I would defend the Guldbrandsen parametrization (or any improvement over it, if it exists) because

• the Gulbrandsen parametrization associated with a full conductor fresnel guarantees a plausible material (even if it doesn't mean that you've created a real material).
• the guldbrandsen parametrization is artist friendly enough and linear enough : an edgeTint of [0,0,0] will result in a fallback to a colored dielectric fresnel reflection and any value above that will progressively increase the reflectance towards grazing angle. It will also tint the color towards grazing angle as long as you don't contradict the color provided by R0 (which is a good behavior).
• the full fresnel conductor parametrized by eta/kappa (and therefore by a mapping to guldbrandsen) can be accurate to a scan, as long as you apply the correct conversion to the spectral data (as demonstrated by Naty).

Ultimately I think we're discussing a non issue. Regardless of the method used, I've never had a problem with Fresnel as an artist over the last 15 years in VFX. I've used Schlick, Generalized Schlick and Guldbrandsen for years and in the hands of a good artist the difference is negligible but in the hands of an uninformed artist, I've always encounter better, more realistic results from the "constraint" that Guldbrandsen pushes on people.

[pleprince]

I think it is great that Naty started the conversation, but I don't buy his conclusions. I find @belcour is going in a more interesting direction, especially with the Gulbrandsen re-parameterization.
My experience totally matches @noj86's post.
Speed, parameterization and accuracy are important but they go hand in hand with physical plausibility constraints.
I often joked about revoking someone's look-dev license after having debugged their implausible materials. These errors cost a lot of time and money in VFX and moving away from physical plausibility would clearly be a step backward.

[nickkuk]

Does anybody see how to use any of Schlick's, Gulbrandsen's, Hoffman's, or @belcour's model for a material inside some dielectric medium?

I understand that it could be solved by additional artistic control, but there are models (especially, @belcour's thin film that is also used in Standard Surface) that need access to underlying real/complex IORs.

[nickkuk]

Maybe I should exclude Gulbrandsen's model from my question, because his article contains transformations from (R0, g) to (n, k), so we can use these IORs (they will be "averaged IORs" in some color space).

[niklasharrysson]

Thanks for the excellent feedback so far!

@fpsunflower some quantitative results of what your artists prefer using would be very interesting.

@noj86 @pleprince, I fully agree we need constraints to stay physically plausible, and I think everyone agree we should not move away from this. Parameters added for artistic control should have good defaults and preferably be protected by chains and locks in the UI.

I think the unification of a Fresnel parameterization for real-time vs offline is the most interesting problem to solve. As long as the parameterization is the same everyone can choose what to do internally. With Gulbrandsen we can transform back and forth to physical IORs. @nickkuk made a good point that we still need this in the case of thin-film interference. @belcour how does this hold up with the Gulbrandsen re-parameterization proposed in your work? Admittedly I have not had a chance to deep dive into it yet either.

[pbarla]

@nickkuk You should be careful when using Gulbransen's parametrization when your ambient medium does not have an IOR of 1, since this is a basic assumption made in Gulbransen's paper.

If for instance you assume that your metallic material is coated with a dielectric layer (to make things simpler, let's assume it's not a thin film), then not only will the reflectivity r should differ due to Fresnel transmittances when going from air to the coating medium; but the effect of the edge tint will also be reduced for two reasons. First, at grazing angles, most of the radiance will be reflected by the first interface, hence reducing the usefulness of the edge tint parameter. Second, Snell's law of refraction will make incoming directions less grazing, so that rays will be less likely to reach grazing angles on the second interface...

As far as I know, there has not been much work done on that specific question (I mean in academic research), even though coated metallic materials seem to be useful to model.

[nickkuk]

@pbarla, thanks! I see the complexity of the problem.

What can you say about "larger medium", e.g., metallic material under water? On a such scale we haven't any light transfer problems in a path tracer - only local Fresnel reflections are in question.

[pbarla]

@nickkuk In a larger medium such as water, there is still another issue I forgot to mention: Gulbransen's approach relies on a formulation of Fresnel equations that is exact only for an ambient medium with an IOR of 1. Hence even if you re-derive the approach for a different ambient medium, you will not get a physically exact solution...

[natyh]

I specifically talk about adapting Schlick for external media in my SIGGRAPH 2020 talk. It is possible with a very simple adjustment which gives good accuracy for water and is less accurate for higher-IOR external media (e.g. diamond). I also present an alternative which is more accurate for high-IOR external media but has some other drawbacks. See slides 106-122 here: https://blog.selfshadow.com/publications/s2020-shading-course/hoffman/s2020_pbs_hoffman_slides.pdf

[natyh]

Also regarding having constraints to stay physically plausible, yes, that's the whole point of going with physically motivated models to begin with! This is something I've been advocating since 2004. But in my opinion Gulbrandsen is actually much worse for this than plain Schlick. With Schlick you can set F0 to whatever you like and you will always get a plausible material. Even values between 0.2-0.4 correspond to semiconductors. But with Gulbrandsen it is difficult to set edgeTint so that the result is plausible. Setting edgeTint [0,0,0] will not result in "a fallback to a colored dielectric fresnel reflection", it will (as I clearly show in slides 137-142) result in a bizarre darkening and color-shift at the edge. I suspect that the reason that people say Gulbrandsen is fine is that a lot of these edge effects are barely noticeable due to foreshortening, but if you don't care about edge behavior, why not just stay with Schlick?

[natyh]

And regarding the benefits of Schlick Fresnel for dielectrics, the big benefit here is being able to handle the entire continuum of materials from dielectrics to semiconductors to conductors within a single specular node.

[natyh]

Regarding F90, yes it is non-physical because it doesn't have the "post-dip rise" to white. But the same foreshortening that squeezes the dip itself into a handful of pixels tends to squeeze that "post-dip rise" to nothing. Here's a close-up of a shaderball edge with Gulbrandsen g set to red. The shift to red is very clear, but I can't see any shift from red to white at the edge. There are probably configurations where that is more visible (maybe a large plane seen edge-on?), and I would love to see renders where the "post-dip rise" is visible if anyone has them.